Geodesic
On Gaussian Measure of Balls in a Hilbert Space
Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 2, pp. 382-390

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Let $X$ be a centered Gaussian random vector taking values in a separable Hilbert space $H$, and let $a\in H$. We investigate the behavior of the density and the distribution function of a noncentered ball $\|X-a\|^2$ by means of its Laplace transform and obtain the results with an optimal estimate of the accuracy rate. As a tool we use a “local limit theorems” approach.
Keywords: small balls, Gaussian measure, Hilbert space
Mots-clés : Laplace transform. 
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     author = {L. V. Rozovskii},
     title = {On {Gaussian} {Measure} of {Balls} in a {Hilbert} {Space}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {382--390},
     publisher = {mathdoc},
     volume = {53},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2008_53_2_a13/}
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L. V. Rozovskii. On Gaussian Measure of Balls in a Hilbert Space. Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 2, pp. 382-390. http://geodesic.mathdoc.fr/item/TVP_2008_53_2_a13/